Trigonometry Examples

${(3 x^{- 6} y^{2})}^{- 3}$

Step 1

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(3 \frac{1}{x^{6}} y^{2})}^{- 3}$

Step 2

Combine $3$ and $\frac{1}{x^{6}}$ .

${(\frac{3}{x^{6}} y^{2})}^{- 3}$

Step 3

Combine $\frac{3}{x^{6}}$ and $y^{2}$ .

${(\frac{3 y^{2}}{x^{6}})}^{- 3}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{x^{6}}{3 y^{2}})}^{3}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Tap for more steps...

Step 5.1

Apply the product rule to $\frac{x^{6}}{3 y^{2}}$ .

$\frac{{(x^{6})}^{3}}{{(3 y^{2})}^{3}}$

Step 5.2

Apply the product rule to $3 y^{2}$ .

$\frac{{(x^{6})}^{3}}{3^{3} {(y^{2})}^{3}}$

Step 6

Multiply the exponents in ${(x^{6})}^{3}$ .

Tap for more steps...

Step 6.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{6 \cdot 3}}{3^{3} {(y^{2})}^{3}}$

Step 6.2

Multiply $6$ by $3$ .

$\frac{x^{18}}{3^{3} {(y^{2})}^{3}}$

Step 7

Simplify the denominator.

Tap for more steps...

Step 7.1

Raise $3$ to the power of $3$ .

$\frac{x^{18}}{27 {(y^{2})}^{3}}$

Step 7.2

Multiply the exponents in ${(y^{2})}^{3}$ .

Tap for more steps...

Step 7.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{18}}{27 y^{2 \cdot 3}}$

Step 7.2.2

Multiply $2$ by $3$ .

$\frac{x^{18}}{27 y^{6}}$